Finite Group Databasebeta

← C3⋊(C5⋊(C7⋊D91)) #34062185

Subgroups — C3⋊(C5⋊(C7⋊D91)) #34062185

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C72×C13C211yesmaximal, characteristic, complemented, Hall
2C5⋊(C7⋊D91)—31nomaximal, Hall
3C3⋊(C7⋊D91)—51nomaximal, Hall
4C5×C72×C13D311yescharacteristic, complemented, Hall
5D1365—78nomaximal
6C3×C72×C13D511yescharacteristic, complemented, Hall
7C3⋊(C5⋊(C7⋊D7))—131nomaximal, Hall
8C3×C5×C7×C13D718yescomplemented
9C7⋊D91—151noHall
10D455—218no—
11C3×C5×C72D1311yescharacteristic, complemented, Hall
12C72×C13D1511yescharacteristic, complemented, Hall
13D273—358no—
14C5⋊(C7⋊D7)—391noHall
15C5×C7×C13D2118yescomplemented
16D195—491noHall
17C3⋊(C7⋊D7)—651noHall
18C3×C7×C13D3518yescomplemented
19C5×C72D3911yescharacteristic, complemented, Hall
20D105—918no—
21C3×C5×C13C7⋊D711yescharacteristic, complemented, Hall
22D91—1058no—
23C3×C72D6511yescharacteristic, complemented, Hall
24D65—1471noHall
25C3×C5×C7D9118yescomplemented
26C7⋊D7—1951noHall
27C7×C13D10518yescomplemented
28D39—2451noHall
29D35—2738no—
30C5×C13C3⋊(C7⋊D7)11yescharacteristic, complemented, Hall
31C72D19511yescharacteristic, complemented, Sylow
32D21—4558no—
33C3×C13C5⋊(C7⋊D7)11yescharacteristic, complemented, Hall
34C5×C7D27318yescomplemented
35D15—6371noHall
36D13—7351noHall
37C3×C7D45518yescomplemented
38C3×C5C7⋊D9111yescharacteristic, complemented, Hall
39D7—13658no—
40C13C3⋊(C5⋊(C7⋊D7))11yescharacteristic, complemented, Sylow
41D5—19111noHall
42C7D136518yescomplemented
43D3—31851noHall
44C5C3⋊(C7⋊D91)11yescharacteristic, complemented, Sylow
45C3C5⋊(C7⋊D91)11yescharacteristic, complemented, Sylow
46C2—95551noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C2
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×C72×C13C2semidirect
4. C5×C72×C13D3semidirect
6. C3×C72×C13D5semidirect
8. C3×C5×C7×C13D7semidirect
11. C3×C5×C72D13semidirect
12. C72×C13D15semidirect
15. C5×C7×C13D21semidirect
18. C3×C7×C13D35semidirect
19. C5×C72D39semidirect
21. C3×C5×C13C7⋊D7semidirect
23. C3×C72D65semidirect
25. C3×C5×C7D91semidirect
27. C7×C13D105semidirect
30. C5×C13C3⋊(C7⋊D7)semidirect
31. C72D195semidirect
33. C3×C13C5⋊(C7⋊D7)semidirect
34. C5×C7D273semidirect
37. C3×C7D455semidirect
38. C3×C5C7⋊D91semidirect
40. C13C3⋊(C5⋊(C7⋊D7))semidirect
42. C7D1365semidirect
44. C5C3⋊(C7⋊D91)semidirect
45. C3C5⋊(C7⋊D91)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×C72×C132
C5⋊(C7⋊D91)3
C3⋊(C7⋊D91)5
D13657
C3⋊(C5⋊(C7⋊D7))13